a: Xét tứ giác OBAC có 

\(\widehat{OBA}+\widehat{OCA}=180^0\)

Do đó: OBAC là tứ giác nội tiếp

a) \(\dfrac{A}{x-2}=\dfrac{x^2+3x+2}{x^2-4}\)

\(\Leftrightarrow\dfrac{A}{x-2}=\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x-2\right)\left(x+2\right)}\)

\(\Leftrightarrow\dfrac{A}{x-2}=\dfrac{x+1}{x-2}\Leftrightarrow A=x+1\)

b) \(\dfrac{M}{x-1}=\dfrac{x^2+3x+2}{x+1}\)

\(\Leftrightarrow\dfrac{M}{x-1}=\dfrac{\left(x+1\right)\left(x+2\right)}{x+1}\)

\(\Leftrightarrow\dfrac{M}{x-1}=x+2\Leftrightarrow M=\left(x-1\right)\left(x+2\right)=x^2+x-2\)

Ta có: \(\left\{{}\begin{matrix}p+e+n=52\\p=e\\p+e-n=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2n=36\\p=e\\p+e+n=52\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}n=18\\p=e=17\end{matrix}\right.\)

Câu 3:

a) 

CTPT xủa X là C_nH_2n+2O

\(n_{CO_2}=\dfrac{8,96}{22,4}=0,4\left(mol\right)\Rightarrow n_{C_nH_{2n+2}O}=\dfrac{0,4}{n}\left(mol\right)\)

=> \(n_{H_2O}=\dfrac{\dfrac{0,4}{n}.\left(2n+2\right)}{2}=\dfrac{0,4}{n}\left(n+1\right)\left(mol\right)\)

Mà \(n_{H_2O}=\dfrac{9}{18}=0,5\left(mol\right)\)

=> n = 4

=> CTPT: C₄H₁₀O

b) \(n_{C_4H_{10}O}=\dfrac{0,4}{4}=0,1\left(mol\right)\)

=> m = 0,1.74 = 7,4 (g)

c)

(1) \(CH_3-CH_2-CH_2-CH_2OH\)

(2) \(CH_3-CH_2-CH\left(OH\right)-CH_3\)

(3) \(CH_3-C\left(CH_3\right)\left(OH\right)-CH_3\)

(4) \(CH_3-CH\left(CH_3\right)-CH_2OH\)

(5) \(CH_3-CH_2-CH_2-O-CH_3\)

(6) \(CH_3-CH\left(CH_3\right)-O-CH_3\)

(7) \(CH_3-CH_2-O-CH_2-CH_3\)

d)

X là \(CH_3-C\left(CH_3\right)\left(OH\right)-CH_3\) (2-metylpropan-2-ol)

1) \(A=\dfrac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{x\sqrt{x}-1}:\dfrac{\sqrt{x}-1}{5}\)

        \(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{5}{\sqrt{x}-1}\) \(=\dfrac{5}{x+\sqrt{x}+1}\)

2) Ta thấy \(x+\sqrt{x}+1=\sqrt{x}\left(\sqrt{x}+1\right)+1>1\forall x\)

\(\Rightarrow A< 5\)

1/ \(n_S=\dfrac{6,4}{32}=0,2;n_{H_2SO_4}=\dfrac{14.70\%}{98}=0,1\)

Bảo toàn nguyên tố S : \(n_S=n_{H_2SO_4\left(lt\right)}=0,2\)

Mà thực tế chỉ thu được 0,1

=> \(H=\dfrac{0,1}{0,2}.100=50\%\)

2/ \(n_{N_2}=0,2\left(mol\right);n_{H_2}=0,3\left(mol\right);n_{NH_3}=0,15\left(mol\right)\)

PTHH: \(N_2+3H_2\rightarrow2NH_3\)

Lập tỉ lệ : \(\dfrac{0,2}{1}>\dfrac{0,3}{3}\)=> Sau phản ứng N2 dư, tính theo số mol H2

=> n NH3(lt)= \(\dfrac{0,3.2}{3}=0,2\left(mol\right)\)

Mà thực tế chỉ thu được 0,15 mol 

=> \(H=\dfrac{0,15}{0,2}.100=75\%\)

Câu 2:

\(R1=R_{nt}-R2=9-6=3\Omega\)

\(=>R_{ss}=\dfrac{R1\cdot R2}{R1+R2}=\dfrac{3\cdot6}{3+6}=2\Omega\)

Chọn A